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Research Paper

Experimental investigation on heat transfer characteristics of plat heat exchanger applied in organic Rankine cycle (ORC) Dong Junqi a,⇑, Zhang Xianhui b, Wang Jianzhang a a b

Zhejiang Yinlun Machinery Co., Ltd, Tiantai, Zhejiang 317200, China School of Foreign Languages, Qingdao University of Science and Technology, Qingdao, Shandong 266042, China

h i g h l i g h t s Engine waste heat recovery ORC system. Experimental study the heat transfer. Single phase convective heat transfer empirical equation. R245fa evaporation boiling heat transfer empirical equation is given.

a r t i c l e

i n f o

Article history: Received 9 August 2016 Revised 9 October 2016 Accepted 30 October 2016 Available online 1 November 2016 Keywords: Waste heat recovery Organic Rankine cycle Plate type heat exchanger R245fa Heat transfer Correlation equation

a b s t r a c t Diesel engine waste heat recovery system based on the organic Rankine cycle (ORC) has been widely studied and developed by more and more researchers in the world. The brazing plate type heat exchangers (PHE) are widely used in the ORC system, especial in the diesel engine waste heat recovery ORC. This paper describes experimentally study the single phase and boiling heat transfer characteristics of three types of working fluid on PHE’s surfaces. These working fluids are water, 50% coolant and R245fa. The single phase convective heat transfer dimensionless empirical equation for the three types working fluid on three different chevron angle plate surfaces is provided, which has the mean absolute error 9.7% in the range Re = 250–7000 and Pr = 2.0–12.0. And the evaporation heat transfer empirical equation for the Organic fluid R245fa is given with the mean absolute error 9.97%, which can predict the 95% of the test data with the error less than ±20%. Ó 2016 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction In recent years, harnessing the renewable energies and waste heat recovery have received growing attention in order to reduce the consumption of fossil fuels and diminish the environmental pollution. Organic Rankine cycle (ORC) is a reliable technology for conversion of these low-grade heat sources into electricity [1–3]. The ORC employs organic fluid as the working media and shows the unique advantage as the working media (refrigerator, R245fa, R134a) with low evaporate pressure, evaporate temperature and higher density which could reduce ORC system size. The low-grade heat sources include the industry waste heat water and exhaust gas. Up to now, the diesel engine has been one of the most widely applied machine in generating the power through consumption ⇑ Corresponding author.

the oil or liquid nature gas (LNG). However, the efficiency of diesel is only about 40% in the past twenty years, and there is above 50% energy emitted to environment as waste heat [4]. ORC technology has drawn many researchers to study the application in the diesel waste heat recovery due to the fuel efficiency improvement requirement. The diesel waste heat mainly lies in the jacket coolant heat, exhaust gas, charge air. Considering the heat grade and heat quantity are different in the jacket coolant (about the 90– 100 °C), exhaust gas (300–400 °C), how to effectively use the two types of waste heat of diesel is also one of the ORC study content. One of the ORC systems which absorbs the diesel waste heat of the jacket coolant and exhaust gas [5,6], is shown in Fig. 1. In ORC system, there are at least two heat exchangers, the evaporator and the condenser. In some ORC systems of diesel waste heat recovery, the pre-heater is also included to reasonably utilize the space and reduce the ORC system size. Plate type heat exchangers (PHE’s) were widely used in many industry fields for both single and two phase flow duties, such as the refrigeration, heating

E-mail address: [email protected] (J. Dong). http://dx.doi.org/10.1016/j.applthermaleng.2016.10.190 1359-4311/Ó 2016 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Nomenclature A b Bo cp dh Em Eab,m G h ifg m n Pr Q q00 Re t U UA um DTLMT x v k

heat transfer area, m2 mean flow channel gap, mm boiling number specific heat capacity, J/kgK hydraulic diameter, mm mean error absolute mean error mass flux, kg/m2s heat transfer coefficient, W/m2K enthalpy of vaporization, J/kg mass flow rate, kg/s total number of test data Prandtl number heat rejection power, W heat flux, W/m2 Reynolds number temperature, °C overall heat transfer coefficient, W/m2K total heat transfer coefficient, W/K mean velocity in chevron channel, m/s log mean temperature difference, °C refrigerator dryness degree Kin. viscosity, m2/s thermo conductivity, W/mK

and cooling, and residential heat pump application [7]. Some basic features of PHE’s include high effectiveness and compactness, flexibility for desire load and pressure drop, and cost competitiveness. The PHE’s are generally more thermally efficient than their shell-and-tube counterparts, particularly for liquid-liquid, liquidtwo phase application. And the PHE’s can much reduce the Organic working fluid charge, which can reduce the ozone-depletion from the environment protection standpoint. The reduction of working media in the ORC system bring the obvious cost down. The augmented heat transfer performance is mainly due to the complex channel geometry which promotes a high degree of turbulence of the flow, especially for the single phase flow. The single-phase heat transfer characteristics for the PHE’s were experiment investigated by many researchers in the past several decades. Emerson [8,9] first investigated the laminar and transition region flow for the chevron type plate heat exchanger. Maslov and Kovalenko [10] provided the classic empirical correlation to predict the heat transfer performance of plat heat exchanger, in which the test sample has the chevron angle 60° and the Re = 50–20,000. Talik et al. [11] gave the heat transfer and pressure drop characteristics use the water as the working fluid and give the single phase heat transfer correlation with the chevron angle of 60°. Khan et al. [12] experimental investigated the single phase heat transfer coefficient using the water as the working fluid for three types of chevron angle and provided the correlation to predict the heat transfer performance in the Re = 500–2500. Longo and Gasparella [13] used the water as working fluid and developed the Nusselt number correlation for the herringbone type PHE with the chevron angle of 65°. Tovazhnyanski et al. [14] investigated thermo-hydraulic characteristics of PHE with different chevron angles. However, it should be noted that most of previous studies provide only partial details on test conditions and plate geometry. The enhancement heat transfer characteristics of PHE’s could be fully used if the plate detail geometries are available. Also, it can be seen that most literatures’ empirical correlations used the water as the working fluid.

u b d

g q

enlargement factor plate chevron angle, ° plat thickness, m viscosity, kg/sm density, kg/m3

Subscripts 1 inlet port 2 outlet port ab absolute ave average c cold side etd entrance temperature difference, °C eq equivalent exp experiment f saturation liquid g saturation vapor h hot side in inlet i hot or cold side m mean max maximum min minimum pre predicted

It is very necessary to do verification for prediction accuracy of the correlation when the correlations are applied in the ORC plate heat exchanger in which the R245fa is used as the working media. And the two-phase evaporator PHE’s has become widely studied since the semi-welded and brazed PHE’s got widely application in refrigerator industry. Although there are many studies for the PHE’s evaporator, it is not yet extensive. Fundamental understanding of the flow boiling is still limited, due to the complex nature of two-phase flow. Practical application and PHE’s evaporator design process require quantitative prediction the heat transfer coefficient of the flow boiling. Up to today, the heat transfer coefficients are obtained mainly depend on the real test and the experiment correlation. Yan and Lin [15] provided the evaporation heat transfer coefficient and pressure drop for refrigerant R-134a flowing in three types of structure plate heat exchanger according to the experiment test results and gave the experiment correlations, Han et al. [16] published the predicted equations using the R22 and R410A as the refrigerator, the test samples have three different types of chevron angle, 45°, 35° and 20°. The deviation between correlation and experimental data are within ±25%. Sterner and Sunden [17] studied the ammonia boiling characteristics and proved three Nusselt empirical correlations for different PHEs using the multiple liner regression analysis. However, in the ORC systems, the PHE’s applications are quite different from the traditional application, such as the refrigeration industry and food industry. First, the difference of diesel waste heat recovery ORC system lies in the working fluid. The diesel ORC use 50% coolant (50% water and 50% ethylene glycol), water and R245fa as the heat transfer working fluid. The 50% coolant is used as the jacket hot source media, R245fa as the ORC system organic fluid, and the water as cold side fluid of ORC condenser. However, it is difficult to find the heat transfer characteristics of these fluids in public literature, especially those of the 50% coolant and R245fa. The flow and heat transfer characters of R245fa with the lower flow velocity have much different with those of the ordinary fluid with higher

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Fig. 1. Engine waste heat recovery ORC system and ORC test rig photo, (a) ORC system schematic, (b) engine ORC test rig photo.

velocity in the flow passes or channels. And the difference is much bigger in the evaporator of ORC system because the organic fluid absorbs higher temperature hot source than those of the compression refrigeration and air condition systems. And the organic fluid evaporation boiling takes place under high saturation temperature and higher pressure. Does the R245fa evaporation performance under higher pressure (7–13 bar) and higher temper (70–110 °C) have the same characteristics with other refrigerator under the low pressure (1–3 bar) and lower temperature (0–10 °C)? This question is another important driving force for this experiment study. So, the present work mainly studies the PHE’s heat transfer characteristics for the three types of working fluid (water, 50% coolant and R245fa) which are widely applied in diesel waste heat recovery ORC system. And the heat transfer performance is studied on three types of the different angles plat surface. The paper will provide the heat transfer empirical correlation which is the most useful for the engineers or designers when they do the PHE’s design or the diesel waste heat recovery ORC system optimization in the practical application.

2. Experiment apparatus and procedures 2.1. Diesel waste heat recovery ORC system There are two parts of waste heat that can be used as the ORC heat source in the diesel waste heat recovery (WHR) system. From Fig. 1, it can be seen that the 50% coolant first absorbs the jacket waste heat of engine to keep the engine in a constant reasonable temperature range. Then, the exhaust gas waste heat is absorbed by the coolant through the exhaust gas heat exchanger C. The coolant with higher temperature enters the evaporator D and preheater E. In the heat energy transfer process, the coolant is used as the media, which transmit the diesel waste heat to the ORC system working fluid R245fa. In the ORC system, the organic fluid R245fa with higher working pressure absorb the diesel waste heat in the pre-heater E and evaporator D. After absorbing the waste heat, the liquid R245fa fluid becomes the higher temperature and higher pressure vapor and enters the expander G, which undertakes the heat energy translate into machine power function, and the expander connects with a direct-current generator, then the

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Table 1 Specification of different measuring devices. Devices

Type

Uncertainty (k = 2)

Range

Application

Thermometers Pressure Abs. Pressure Abs. Diff. Pressure Diff. Pressure Mass flow meters Mass flow meters

RTD100 Strain-gage Strain-gage Strain-gage Strain-gage Coriolis effect Coriolis effect

0.1 k 0.075% 0.075% 0.075% 0.075% 0.1% 0.1%

0–120 °C 0–0.6 MPa 0–1.2 MPa 0–100 kPa 0–50 kPa 0–2000 kg/h 0–15,000 kg/h

Water, coolant, R245fa Water coolant R245fa Water and coolant R245fa R245fa Water, coolant

R245fa vapor enters the condenser F, in which the R245fa vapor becomes the liquid through transfer heat energy to cool water which comes from outside cooling tower. In the ORC system, the plate type heat exchangers are applied as the pre-heater, evaporator and condenser due to the compactness and lower refrigerator charge. The heat transfer fluids are the 50% coolant, water and R245fa. In the pre-heater and evaporator, the two side fluids are the R245fa and coolant; and in the condenser, the two side fluids are R245fa and water.

Fig. 2. Water test system schematic for PHE’s using the equal Reynolds method.

2.2. Plate type heat exchanger test apparatus The main aim of the study is to study the heat transfer coefficients of three types of working fluid, water, 50% coolant and Organic fluid R245fa, on three different chevron PHE’s surfaces. First, the study investigates the water heat transfer character under different flow velocity by the experiment using the Revised equal Reynolds method and gets the heat transfer coefficients. Then, the experiment investigates the heat transfer performances of the 50% coolant and single-phase R245fa on three types of PHE’s surface using the heat resistance separating method because the heat transfer resistance of water side is known according to the first step study results. At last, the boiling heat transfer coefficients of R245fa under different heat flux and mass flow rate with two different evaporation pressure are tested. The test accuracies of the most sensors were listed in Table 1. In Fig. 2, the water is used as the cold and hot working fluid of PHE’s two sides during the test process. This test rig is special test for the heat exchanger which have the same flow pass and the same structure parameters like the PHE’s and plate fin heat exchangers. In the test system, water is the only fluid in the loop and use one flow meter. The reason to choose the water as the working fluid is that the property of water has not obvious change in a smaller temperature different range. And the heat transfer coefficients of water side are much bigger than those of other fluid under the same flow velocity. In this test system, the water is heated by electric heater and pumped into the test sample, then the water is cooled by a cool fan which can be adjusted the speed to control the water inlet temperature of the test sample cold side. This can keep the two sides of test sample have the same velocity. During the test process, two side fluids flow in the counter flow

Fig. 3. Water and coolant test rig schematic.

J. Dong et al. / Applied Thermal Engineering 112 (2017) 1137–1152 Table 2 Geometric characteristics of chevron plate in the present study. Lw, Plate width, mm Lp, plate port to port channel length, mm Leff, plate effective channel length, mm Dp, port Diameter, mm N, Number of the plate layer, b, mean flow channel gap, mm d, plate thickness, mm pc: plate corrugation pitch, mm u, Enlargement factor b; plate chevron angle

310 624 544 40 21 2.35 0.3 8 1.16 60°, 60°/30°, 30°

and the average temperature difference of two sides was controlled in 5 °C range to keep two sides water flow at the approximate equate average Re. In the water and coolant test rig, the 50% coolant is used as the hot side with a Electric heater. The water is used as the cold side

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fluid, in which an adjusted cool fan and an electric heater are used to control the inlet temperature of the test sample. The flow rate of the water and coolant side is controlled respectively by a variable frequency motor and pump. The two Coriolis effect flow meters are used and recorded the mass flow rate in the two sides. The temperatures of the test sample inlet and outlet are recorded by the thermal resistance thermometers (RTD), the inlet pressure and the pressure drop are recorded by the pressure sensors and pressure difference transmitters. The organic fluid R245 single phase heat transfer test and boiling test in the pre-heat and evaporator PHE’s are fulfilled in the ORC test rig. In the test system, the ORC system efficiency, expander efficiency and evaporator performance and so on can be done by through adjusting the different parameters. For example, by adjusting the open or close status of bypass valve1 and bypass valve 2, we can do the ORC testing or evaporator boiling test.

Fig. 4. ORC and R245fa fluid test schematic and real photo picture, (a) test schematic, (b) photo picture.

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In the whole test system, there are 4 sub-systems. They are the pre-heater sub-system, water heater evaporator sub-system, condenser cooling sub-system and ORC organic fluid loop system. In ORC loop sub-system, the organic fluid R245fa is successively pumped into the pre-heater, test sample (evaporator) in which the R245fa absorbs the heat energy and become the vapor with higher temperature and higher pressure. If bypass valve 2 is opened, the R245fa vapor will enter the expander and bring the electric power by a DC generator. In this study, the main function is to do the pre-heater test and evaporator boiling test, the bypass valve2 before the expander is closed and bypass valve 1 is opened. And the bypass valve 1 can adjust the organic fluid flow rate and the pressure of evaporator. The water sub-system of the pre-heater is used to control the R245fa inlet temperature of evaporator by adjusting the pre-heat sub-system electrical heater power and coolant temperature of receiver. During the test process, the inlet temperature of R245fa should be kept in sub-cool status and the degree of sub-cooling is less than 2 °C. At the same time, the outlet temperature of test sample should be kept superheat condition and the superheat degree was less than 5 °C. In the test process, the R245fa mass flow rate and the evaporator pressure should be kept constant by adjusting the coolant flow rate of the coolant sub-system, the bypass valve1 opening, and the condensing pressure of condenser. As for the R245fa parameter strong coupling phenomena, the testing parameter adjustment should take more time.

(a)

During the test, the sufficient testing time is given to the system to achieve steady state condition. The flow rate, temperature and pressure at all inlets and outlets of the test sample PHE are monitored. All test data and signal are scanned and recorded one time in one second. If all the temperature of exit and inlet change rate are less than 0.02 °C/s, the test steady conditions are got and these test data are recorded and saved in the 90 s. Then the test turn on the next test condition. In every condition, the average of the recoded 90 data is treaded as the last test data (see Fig. 3).

2.3. Plate type heat exchanger test samples Brazed plat type heat exchanger with commercial chevron plates are tested in this study. Important geometric characteristics of the chevron plat as defined in Ayub [18] are shown in Table 2 with parameters defined in Fig. 4. And Table 2 presents the geometric details of the chevron plates used in the present study. Fig. 4 also provide the real photo for the testing sample and cut surface of the middle section in two brazed layers. These parameters include the plate chevron angle, corrugation depth and corrugation pitch vary for different plates. There are three types of plate with different chevron angles, respectively 60°, 60°/30°, 30°. During the test data reduction, the mixed chevron angle 60°/30° is tread as 45°. Each sample has one pass which has 10 channels, and the two sides fluid are counter-flow in the test process.

(b)

A-A

(c) Fig. 5. PHE’s plate photo and geometry parameters definition, (a) plate photo, (b) cut middle section for brazing point, (c) plate geometry parameters definition.

J. Dong et al. / Applied Thermal Engineering 112 (2017) 1137–1152

Fig. 6. Heat transfer coefficient with velocity, (a) fluid is water, (b) fluid is 50% coolant, (c) fluid is R245fa.

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Fig. 7. Nusselt number with Reynolds, (a) fluid is water, (b) fluid is 50% coolant, (c) fluid is R245fa.

J. Dong et al. / Applied Thermal Engineering 112 (2017) 1137–1152

2.4. Data reduction The main parameters of considered problem are the Reynolds number Re, heat transfer coefficient h and the Nusselt number Nu. They are defined as follows:

Re ¼

um dh

Nu ¼

ð1Þ

m

heat, Cp, is very constant in a smaller temper range, the water heat rejection Qh is used as the test sample heat rejection power. The overall heat transfer coefficient U is can be gotten from,

UA ¼ Q h =ðDT LM Þ

DT LM ¼

ð7Þ

ðDT max DT min Þ Ln DDTTmax

ð8Þ

min

The total heat transfer coefficient UA can be expressed,

h dh k

ð2Þ

The experiment data are reduced to obtain the heat transfer coefficient of one side. As for the single phase fluid flow, the heat transfer coefficient are obtained for the water, 50% coolant fluid and organic fluid R245fa using the different method. For water, the data reduction applied the equal Re method. For the coolant and R245fa, the thermal resistance separating method is applied during the data reduction. For the plate of the test sample, the hydraulic diameter of the channel is defined as [13], which is also the characteristic length for the Reynolds and Nusselt number:

dh ¼ 2b=u

ð3Þ

First, to get the heat transfer character of water on the plate corrugation surface wall, the test apply the approximate equate Re which can keep the two side with the equal heat transfer coefficient. The property of fluid is determine by the average temperature of the inlet and outlet on the one side fluid, the average temperature is give by:

tave ¼

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t1i þ t2i 2

ð4Þ

The heat and cold load of the test sample are expressed:

Q c ¼ mc C p ðt c2 t c1 Þ

ð5Þ

Q h ¼ mh C p ðt h1 t h2 Þ

ð6Þ

For all the test data, the heat balance is less than 3%, ðQ h Q c Þ=Q h < 3%: As for the water property, such as the specific

1 1 1 d ¼ þ þ UA hc A hh A k A

ð9Þ

The heat transfer area is equal in the both side of PHE’s and the average Re is approximate equal as the two side fluids, water, have the same average flow velocity in each channel. And the average temperature difference of two side is less than 5 °C which can keep the water thermo-physical property difference has very little effect on the heat transfer coefficients. So the heat transfer coefficient, h, is approximate equal in both sides.

1 1 1 d ¼ h 2 U k

ð10Þ

Second, for the coolant and R245fa test data, the thermal resistance separating method is applied.

1 1 1 d ¼ hc U h h k

ð11Þ

In Eq. (11), the water heat transfer coefficient hh is known according to Eq. (10) and water heat transfer coefficient regress equation. In the R245fa boiling test, the heat transfer coefficients are also gotten by using thermal resistance separating method, in which the heat transfer coefficient of water side is known according to the first step test data and regress equation. 2.5. Experiment uncertainty To estimate the uncertainties of the experimental results, an uncertainty analysis is carried out. Moffat [19] proposed a procedure outline and formula to evaluate the uncertainty. The experi-

Fig. 8. Heat transfer coefficient with Re for 3 types fluid.

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ment errors in the Reynolds number (Re), Nusselt number (Nu), heat transfer coefficient (h) are estimated by using Eqs. (1), (2), (10) or (11). And the uncertainties associate with the related dependents variable. If the R+ is a function of the independent variables X1, X2, . . . Xn and w1, w2, . . . wn are the uncertainties in the independent variables, the uncertainty in the dependent variable W+R is given by:

W Rþ ¼

þ 2 þ 2 þ 2 !1=2 @R @R @R w1 þ w2 þ þ wn @X 1 @X 2 @X n

and temperature were found to be ±2.1% and ±1.2%, respectively. Based on these errors, the maximum uncertainty of ±8.2% exists in calculated value of Nu. For the boiling test, the maximum uncertainty is ±13.7% as for the R245fa fluid property in phase change zone.

3. Results and discussion

ð12Þ

According to the formula, after counting for the errors in the heating and cooling water, coolant and single phase R245fa, the maximum errors in the primary measurement of mass flow rate

3.1. Single phase heat transfer character for three types of plate structure The experiment results about the heat transfer performance for the three types of plate using water, 50% coolant and R245fa as

Fig. 9. Comparisons for thermo physical property, (a) thermal conductivity, (b) Kin viscosity.

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working fluids are reported and discussed here. For the single phase fluid heat transfer, the velocity and geometry parameters are the most important factors on the heat transfer performance (see Fig. 5). Fig. 6 gives the changing curves for the heat transfer coefficients with different velocity in the corrugation channel for three chevron angles b, 60°, 60°/30°, 30°. From Fig. 6a and b, it can be seen the velocity and chevron angle b have very obvious effects on the heat transfer. The heat transfer coefficients will increase with the velocity increases and the chevron angle b increases. For the three types of plat, the chevron angle b = 60° has the biggest heat transfer coefficient and the b = 30° has the smallest heat transfer coefficient under the same velocity. However, when the organic fluid R245fa is the testing fluid, the effects of chevron angle b on heat transfer become very smaller compared to those of the working fluids of the water and 50% coolant. In Fig. 6c, it describes the effects of three chevron angles on the heat transfer coefficients under different velocity. As for R245fa, the chevron angle b = 60° and the chevron angle b = 60°/30° plat almost have the similar heat transfer coefficients under the same velocity. To further describe the heat transfer character for the different chevron angles and different flow conditions, the dimensionless parameter Re and Nu are used. Fig. 7 gives the three types working fluid heat transfer performance for different Re and different chevron angles b. From the three figures about Re and Nu, we can see that no matter it’s water or 50% coolant, the Nu will increase with the Re increasing. And the increasing of chevron angle brings the obvious improvement of heat transfer performance Nu under the same Re. At the same time, the increasing rate of Nu will become bigger with the chevron angle b increasing. However, in Fig. 7c about the trend of Nu with Re for the R245fa fluid, we can see there is no particular improvement for the Nu with the chevron angle increasing under the same Re. This no obvious increasing phenomenon has much difference with coolant and water under high Re region. The reason may be is that the R245fa fluid working condition in the test is low Re region. In the low Re region, the enhanced heat transfer mechanism due to geometry parameter change will become smaller.

In Fig. 8, it clearly shows that the increasing rate of heat transfer coefficients has much difference for three different types of working fluid, water, 50% coolant and R245fa. The heat transfer coefficients for water and 50% coolant almost have the same trend with the Re increasing. But for R245fa, under the same Re, the heat transfer coefficients are much lower than those of the water and 50% coolant. However, from the perspective of heat transfer coefficient increasing rate, R245fa has a very much bigger increasing rate under the low Re region, the increasing rate is almost equal 1. The reasons may lie in the fact that R245fa has very smaller physical property parameters compared to the water and 50% coolant, such as the viscosity, density, thermal conductivity and Pr. The parameters have much bigger effects on the flow and heat transfer character. Fig. 9a and b gives the much difference for the viscosity and thermal conductivity for three types of fluid under different temperature. 3.2. Empirical correlation for the single phase heat transfer To facilitate the application of the plate heat exchangers as preheaters, condensers and evaporators in the diesel engine waste heat recovery organic Rankine cycle (ORC) system, the correlation equation for dimensionless heat transfer is provided. The correlation equation is obtained by the multiple regression method based on the test data. For the three working fluid, water, 50% coolant and R245fa, and three chevron angle plate heat exchangers, the heat transfer correlation equation is given:

Nu ¼ 0:964 Re0:671 Pr0:32

b 180

1:022 ð13Þ

The correlation equation can meet the 90% test data prediction errors within ±15%. Fig. 10 gives the comparison of the prediction Nu using the regression Eq. (13) with the test Nu data. The application range should meet the confine that the Re = 250–7000 and Pr = 2.0–12.0. To evaluate the predict precision, the definitions for the mean error and mean absolute error [7] are given:

Mean error : Em ¼

1 X Nupre Nuexp n Nuexp

Fig. 10. Comparison of prediction Nu using Eq. (13) and with experiment data.

ð14Þ

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5.5

Comparisons for β: 60°---Water

5.0

Ln(Nu)

4.5 4.0 3.5 Test Data Talik[11] Garcia[20]

3.0

Present Correlaon Maslov and Kovalenko[10]

2.5 0

1000

2000

3000

4000

5000

6000

7000

Re

(a) 5.5

Comparisons for β: 60°---50%Coolant

5.0

Ln(Nu)

4.5 4.0 3.5 3.0

Test data

Present Correlaon

Talik[11]

Maslov and Kovalenko[10]

Garcia[20]

2.5 0

500

1000

1500

2000

2500

3000

Re

(b) 5.0

Comparisons for β: 60°---R245fa

4.5

Ln(Nu)

4.0 3.5

3.0 2.5

Test Data

2.0

Present Data

Talik[11]

Maslov and Kovalenko[10]

Garcia [20]

1.5 0

200

400

600

800

1000

Re

(c) Fig. 11. Comparison for different correlation predicting data with test data.

1200

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Fig. 12. Heat rejection with mass flow rate for different evaporation pressure, (a) evaporation pressure is 400 kPa, (b) evaporation pressure is 800 kPa.

Mean absolute error : Em:ab ¼

1 X Nupre Nuexp n Nuexp

ð15Þ

For the correlation Eq. (13), average error of this correlation is 1.7%, mean absolute error is 9.7% for all the data. To validate the present empirical correlation for the single phase heat transfer, the comparisons are made for the chevron angle b = 60° using the different research’s correlations. Fig. 11 gives the comparison results between the test data and the prediction using different correlations under different working conditions. From Fig. 11(a) and (b), in which the working fluid are the water and 50% coolant, it can be seen that the present empirical correlation predicted data are consistent with the test data and those of other researcher’s correlation. Comparing the prediction using different researcher’s correlation, the predicted data using the present correlation lie in the middle level under the same working condition. In Fig. 11(c), using the R245fa as the working fluid, we can seen that the present correlation can predict the test

data with very smaller deviation, however, the other researchers’ correlation prediction are bigger than the test data. 3.3. Empirical correlation for the boiling heat transfer For the evaporation heat transfer, there is much difference with the single phase convection heat transfer. To compare the heat transfer performance for the different plat type and different evaporator pressure, the heat rejection per entrance temperature difference, Q =DTetd , is used,

DTetd ¼ Tin;h T in;c

ð16Þ

Fig. 12a and b gives the heat transfer performance of organic fluid R245fa on three types of chevron angle plate surface under evaporator pressure 480–510 kPa and 800—850 kPa. The pictures show that the chevron angle of plate has no obvious effect on the evaporator heat performance under the different evaporator pres-

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Fig. 13. Heat transfer coefficient with Boeq.

Fig. 14. Heat transfer coefficient with heat flux q00 .

sure. And comparing the two pictures, it also can be seen that the trend of heat rejection with R245fa mass flow rate are similar under the two evaporator pressure. Considering the main purpose of this study is to provide a calculation equation for the engineers when they do the heat exchanger design and system optimization. So the authors don’t want to invent the new definition or terminology to describe the evaporator performance. The well-known two-phase parameters are also applied which have been widely used in published papers [20,21]. These two-phase parameters include the two-phase equivalent mass flow rate, equivalent Reynolds, Boiling number, the definition for them are:

2

qf Geq ¼ G41 x x qg Reeq ¼

Boeq ¼

Geq Dh

gf q00 Geq ifg

!0:5 3 5

ð17Þ

ð18Þ

ð19Þ

In present study, the degree of R245fa dryness x is tread as 0.5, due to the dryness of inlet and outlet port of test sample are 0 and

J. Dong et al. / Applied Thermal Engineering 112 (2017) 1137–1152

1151

For 95% the test data, the predict errors of the correlation Eq. (20) are less than ±20%. And the mean error and the mean absolute error for all the data are 0.71% and 9.97%. Fig. 16 is the comparison the correlation Eq. (20) predict Nu with the experiment Nu. 4. Conclusions Experiments have been performed to investigate heat transfer characteristics of the plat type brazing heat exchangers using the water, 50% coolant and R245fa as the working fluids which have been widely applied in waste heat recovery ORC systems. The three types of fluid heat transfer characteristics are reported and the single fluid heat transfer empirical correlation is given including three different chevron angles. Also, the R245fa evaporation performance are investigated as the evaporator, the dimensionless heat transfer correlation is given by multiple regression method. The main conclusions are, Fig. 15. Heat transfer coefficient with Reeq.

1. And the heat transfer coefficient of evaporator is treated as the average heat transfer coefficient in whole evaporator zone with the average dryness 0.5 condition. From Figs. 13–15, it can be seen the plate chevron angle has no obvious effect on the evaporation heat transfer coefficient. But the equivalent Boiling Number, Boeq, and equivalent Reynolds, Reeq, are the important factors on the heat transfer coefficient. With the Boeq and Reeq increasing, the heat transfer coefficient improves quickly. The dimensionless correlation equation for the evaporation heat transfer performance is given by the multiple regression based on the test data. The dimensionless empirical correlation for R245fa is,

Nu ¼ 2:64 Re0:815 Pr0:333 Bo0:343 eq f eq

ð20Þ

The application region for the correlation is the Reeq = 250– 2500.

(1) For the single phase convective heat transfer, in the test range chevron angle 30–60°, the plate chevron angle has an obvious effect on the heat transfer coefficient which will be quickly improved with chevron angle increasing under the same working conditions. (2) In the low Re region, the R245fa as the working fluid, the heat transfer increasing rate is larger than those of water and 50% coolant. (3) The single phase convective heat transfer dimensionless empirical correlation is given in the Re = 250–7000 and Pr = 2.0–12.0 region, the predict mean absolute error is 9.7%. And for the 90% test data, the predict error is less than ±15% (4) The R245fa evaporation characteristics comparisons are given for different evaporation pressure, heat flux q00 and equivalent Reeq. And the evaporation heat transfer empirical dimensionless correlation is given. The predicted absolute error is 9.97% for all the test data. The evaporation correlation can predict the 95% test data with the error less than ±20%.

Fig. 16. Comparison of prediction Nu using Eq. (20) and with experiment data.

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